Adaptive multicenter designs for continuous response clinical trials in the presence of an unknown sensitive subgroup

The partial effectiveness of drugs is of importance to the pharmaceutical industry. Randomized controlled trials (RCTs) assuming the existence of a subgroup sensitive to the treatment are already used. These designs, however, are available only if there is a known marker for identifying subjects in the subgroup. In this paper we investigate a model in which the response in the treatment group $Z^T$ has a two-component mixture density $(1-p)\mathcal N(\mu^C, \sigma^2)+p\mathcal N(\mu^T, \sigma^2)$ representing the treatment responses of \emph{placebo responders} and \emph{drug responders}. The treatment-specific effect is $\mu = \frac{\mu^T-\mu^C}{\sigma}$ and $p$ is the prevalence of the drug responders in the population. Other patients in the treatment group react as if they had received a placebo. We develop one- and two-stage RCT designs that are able to detect a sensitive subgroup based solely on the responses. We also extend them to a multicenter RCTs using Hochberg's step-up procedure. We avoid extensive simulations and use simple and quick numerical optimization methods.